14x=3x^2-5

Solution for 14x=3x^2-5 equation:

14x=3x^2-5

We move all terms to the left:

14x-(3x^2-5)=0

We get rid of parentheses

-3x^2+14x+5=0

a = -3; b = 14; c = +5;
Δ = b2-4ac
Δ = 142-4·(-3)·5
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-16}{2*-3}=\frac{-30}{-6}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+16}{2*-3}=\frac{2}{-6}
=-1/3
$